queuing on election day

This is another blog post about voting. This one focuses on the actual act of voting in all its queuing glory.

Queue basics: the voters are customers who enter the system. The system here is a voting area for a precinct. The voters wait in a queue to cast their votes in voting booths (the servers). The customer arrival rates depend on the time of day, and hence, the system is not stationary.

Let’s look at different ways to look at voting from a queuing perspective.

Let’s start with this article in the Economist that argues that bad weather favors Romney. Here, they focus on how weather affects the voter arrival rates:

To be brutal, a certain amount of bad weather on election day helps conservatives in every democracy. In crude terms, car-driving conservative retirees still turn out in driving rain, when bus-taking lower-income workers just back from a night shift are more likely to give rain-soaked polls a miss. School closures are a particular problem for low-income families or single mothers scrambling to find childcare.

Thus, bad weather may decrease the arrival rate of liberal voters more than of conservative voters.

Ultimately, many people are going to vote. Long lines were a problem in 2004 and 2008, and a few balked at waiting in line. Many places (such as my state of Virginia) offered early voting via absentee ballots to voters in 2008, since the turnout was unprecedented. Waiting in line to vote leads to questions about voting machine allocations and the time it takes to vote.

Muer Yang, Ted Allen, and Michael Fry wrote a paper that focuses on the number of servers and the service times. [Link to press release] They examine how to assign voting machines to precincts to equalize the amount of waiting time between precincts so that some precincts are not plagued with long waiting times while others are not. They do so by noting that voting is not stationary and include  other realistic voting complications:

“[The election board’s] assumptions of those problems are not even close to the real world,” he added, “because [the election board’s traditional] model assumes a stationary voter arrival — that voters arrive at the voting station at the same rate, which is not true. We use simulation models to consider realistic complications, including variables such as voter arrival time, voter turnout, length of time needed to finish a ballot, peak voting times and machine failures.”

The paper hasn’t been published yet, so I don’t know all of the details. To satiate your desire for mathematical details, you can read this paper in the Winter Simulation Conference by Muer Yang, Michael Fry, and David Kelton. They examines how to allocate voting machines (servers) to voting precincts in an equitable manner.  There are many ways to evaluate equity. Here, the authors use the average absolute differences of expected waiting times among precincts as a proxy for “equity.”  They provide a heuristic that uses a factorial experimental design and show that this heuristic outperforms the “utilization-equalization” method. The  “utilization-equalization” method is another proxy for voter equity that “equalizes the utilization of voting machines rather than equalizing waiting times of voters. Moreover, the utilization rate is obtained by traditional queueing theory, which assumes stationary arrivals and steady-state operating conditions.”

Initially, I thought that so many people voting early via absentee ballot or just early voting would mean fewer long lines in a queue. This is not necessarily the case. Early voting in South Florida and Ohio has been plagued with long lines (up to six hours). Hopefully, this means that fewer people will be in line on Election Day. I haven’t heard yet if state budget cuts will lead to poorly staffed voting precincts, which will in turn lead to long lines on Election Day even if the turnout isn’t record-setting.

All those voter ID laws were supposed to cut down on voter fraud. In a queuing context, that means that the new laws would slightly reduce the voter arrival rates. Carl Bialik wrote a nice article in the WSJ [Link] about voter fraud and whether voter ID laws would make much of a difference. The short answer is that they don’t. Fraud is hard to detect, and when it has been detected, it has most often occurred with absentee ballots (no ID needed to vote absentee) and during voter registration.

How long did you wait in line to vote?